Solve for $x$ : $5x^2 - 40x - 100 = 0$
Solution: Dividing both sides by $5$ gives: $ x^2 {-8}x {-20} = 0 $ The coefficient on the $x$ term is $-8$ and the constant term is $-20$ , so we need to find two numbers that add up to $-8$ and multiply to $-20$ The two numbers $-10$ and $2$ satisfy both conditions: $ {-10} + {2} = {-8} $ $ {-10} \times {2} = {-20} $ $(x {-10}) (x + {2}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -10) (x + 2) = 0$ $x - 10 = 0$ or $x + 2 = 0$ Thus, $x = 10$ and $x = -2$ are the solutions.